Q81 / 160 · JIPMER 2004 · Physics

The dimensions of gravitational constant are

  • A
    $\left[\mathrm{ML}^3 \mathrm{~T}^{-2}\right]$
  • B
    $\left[\mathrm{M}^{-1} \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$
  • C
    $\left[\mathrm{ML}^{-2} \mathrm{~T}^2\right]$
  • Correct answer
    D
    $\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$

Solution

From the formula $G=\frac{F R^2}{m_1 m_2}$ $\begin{aligned} & G=\frac{\text { Dimensions of dimensions of force } F \times \text { dimension of }(R)^2}{\text { dimensions of mass } M \times \text { dimension of mass } M} \end{aligned}$ $=\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^2\right]}{[\mathrm{M}][\mathrm{M}]}=\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$

Hence, the correct answer is option: 'D'.

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